Underwater quantum communication has recently been explored using polarization and orbital angular momentum. Here, we show that spatially structured modes, e.g., a coherent superposition of beams carrying both polarization and orbital angular momentum, can also be used for underwater quantum cryptography. We also use the polarization degree of freedom for quantum communication in an underwater channel having various lengths, up to $30$ meters. The underwater channel proves to be a difficult environment for establishing quantum communication as underwater optical turbulence results in significant beam wandering and distortions. However, the errors associated to the turbulence do not result in error rates above the threshold for establishing a positive key in a quantum communication link with both the polarization and spatially structured photons. The impact of the underwater channel on the spatially structured modes is also investigated at different distances using polarization tomography.
Underwater quantum communication has recently been explored using polarization and orbital angular momentum. Here, we show that spatially structured modes, e.g., a coherent superposition of beams carrying both polarization and orbital angular momentum, can also be used for underwater quantum cryptography. We also use the polarization degree of freedom for quantum communication in an underwater channel having various lengths, up to 30 meters. The underwater channel proves to be a difficult environment for establishing quantum communication as underwater optical turbulence results in significant beam wandering and distortions. However, the errors associated to the turbulence do not result in error rates above the threshold for establishing a positive key in a quantum communication link with both the polarization and spatially structured photons. The impact of the underwater channel on the spatially structured modes is also investigated at different distances using polarization tomography.
Abstract Underwater quantum communication has recently been explored using polarization and orbital angular momentum (OAM). Here, we show that spatially structured modes, e.g., a coherent superposition of beams carrying both polarization and OAM, can also be used for underwater quantum cryptography. We also use the polarization degree of freedom to investigate the impact of the channel length on key rates for quantum communication applications. The underwater channel proves to be a difficult environment for establishing quantum communication as underwater optical turbulence results in significant beam wandering and distortions. However, the errors associated to the turbulence do not result in error rates above the threshold for establishing a positive key in a quantum communication link with both the polarization and spatially structured photons. The impact of the underwater channel on the spatially structured modes is also investigated at different distances using polarization tomography.
Light with a complex amplitude structure invokes interesting fundamental properties such as phase and polarization singularities, which also enables novel applications in classical and quantum optical experiments [1]. One feature, namely a twisted phase front and its orbital angular momentum, attracted a lot of attention due its broad range of applications. In the quantum domain, structured photons are highly beneficial since they serve as a physical realizations of high-dimensional states, which allow for example an enlarged information content per single carrier and are known to have a better noise resistance in quantum cryptography applications [2]. At first, I will present a set of laboratory experiments, in which we investigate different quantum cryptographic protocols. Our versatile approach relies on a heralded single photon source, a preparation stage at Alice’s sender, a 1 m-long quantum channel, and a detection stage at Bob’s receiver unit. Because the generation and detection is performed using computer generated, re-programmable holograms displayed on spatial light modulators, the same setup can be used to experimentally survey different quantum key distribution techniques and compare their benefits and deficiencies. The investigated protocols are all based on high-dimensional quantum states and include the seminal protocol of Bennett & Brassard, tomographic protocols, and recently introduced differential phase shift protocols [3,4]. We compare the performance of the different approaches in terms of noise resistance and secret key rates. Our study highlights the benefits of using structured photons and high-dimensional quantum states for different implementations and channel conditions. In a second series of experiments, we get a step closer to real world implementations and investigate long distance and underwater quantum cryptography using high-dimensional quantum information encoded on structured light. We establish an approx. 280m long intra-city quantum link and study the influence of turbulence on achievable key rates [5]. We further test the effect of water turbulences on an underwater quantum channel using twisted photons in an outdoor pool of 3 m length [6]. Although we are able establish a secure channel with three dimensional quantum states, we find mode deformations and vortex splitting due to strong turbulent conditions most probably caused by local variations in temperature. We perform a detailed analysis of the observed turbulence and find that underwater channels may give rise to turbulent conditions that are fundamentally different in terms of temporal and spatial disturbance from those present in a free-space channel. [1] H. Rubinsztein-Dunlop et al. Roadmap on structured light, Journal of Optics 19, 013001 (2017) [2] M. Erhard, R. Fickler, M. Krenn, A. Zeilinger, Twisted Photons: New Quantum Perspectives in High Dimensions, Nature Light: Science & Applications, 7 17146 (2018) [3] F. Bouchard et al. Experimental investigation of quantum key distribution protocols with twisted photons, arXiv:1802.05773 [4] F. Bouchard, A. Sit, K. Heshami, R. Fickler, E. Karimi, Round-Robin Differential Phase-Shift Quantum Key Distribution with Twisted Photons, arXiv:1803.00166 [5] A. Sit et al. High-Dimensional Intra-City Quantum Cryptography with Structured Photons, Optica 4, 1006 (2017) [6] F. Bouchard et al. Underwater Quantum Key Distribution in Outdoor Conditions with Twisted Photons, arXiv:1801.10299
We employ non-diffractive Bessel-Gaussian beams to investigate the effect of oceanic turbulence on quantum communication protocols via behaviors of quantum-channel capacity and trace distance, based on the analytical expression of the phase structure function of an orbital-angular-momentum (OAM) beam in underwater wireless optical communication. Our results show that turbulence conditions with a larger inner-scale and outer-scale factors, higher dissipation rate of kinetic energy, lower dissipation rate of the mean-squared temperature, and smaller temperature-salinity contribution ratio are beneficial to quantum communication performance. Moreover, we show that the distribution protocol may be improved by distributing quantum superposition states instead of OAM eigenstates. We believe our work provides the first theoretical exploration of quantum-channel capacity in underwater OAM quantum communication.
We examine the propagation of optical beams possessing different polarization states and spatial modes through the Ottawa River in Canada. A Shack-Hartmann wavefront sensor is used to record the distorted beam's wavefront. The turbulence in the underwater channel is analysed, and associated Zernike coefficients are obtained in real-time. Finally, we explore the feasibility of transmitting polarization states as well as spatial modes through the underwater channel for applications in quantum cryptography.
Abstract As an emerging channel resource for modern optics, big data, internet traffic and quantum technologies, twisted photons carrying orbital angular momentum (OAM) have been extended their applicable boundary in different media, such as optical fiber and atmosphere. Due to the extreme condition of loss and pressure, underwater transmission of twisted photons has not been well investigated yet. Especially, single-photon tests were all limited at a level of a few meters, and it is in practice unclear what will happen for longer transmission distances. Here we experimentally demonstrate the transmission of single-photon twisted light over an underwater channel up to 55 m, which reach a distance allowing potential real applications. For different order OAM states and their superposition, a good preservation of modal structure and topological charge are observed. Our results for the first time reveal the real transmission performance of twisted photons in a long-distance regime, representing a step further towards OAM-based underwater quantum communication.
Quantum communication has been successfully implemented in optical fibres and through free-space. Fibre systems, though capable of fast key and low error rates, are impractical in communicating with destinations without an established fibre link. Free-space quantum channels can overcome such limitations and reach long distances with the advent of satellite-to-ground links. However, turbulence, resulting from local fluctuations in refractive index, becomes a major challenge by adding errors and losses. Recently, an interest in investigating the possibility of underwater quantum channels has arisen. Here, we investigate the effect of turbulence on an underwater quantum channel using twisted photons in outdoor conditions. We study the effect of turbulence on transmitted error rates, and compare different quantum cryptographic protocols in an underwater quantum channel, showing the feasibility of high-dimensional encoding schemes. Our work may open the way for secure high-dimensional quantum communication between submersibles, and provides important input for potential submersibles-to-satellite quantum communication.